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Clinical Chemistry 25: 2011-2014, 1979;
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Clinical Chemistry, Vol 25, 2011-2014, Copyright © 1979 by American Association for Clinical Chemistry

A statistical method for determining normal ranges from laboratory data including values below the minimum detectable value

JY Tsay, IW Chen, HR Maxon and L Heminger

Determination of normal ranges from laboratory data containing undectable values is a frequently encountered problem in the radioimmunoassay of peptide hormones. In the past, such determinations usually have been based on the mid-point method or the one-end Winsorized method. A graphic method involving the use of probability paper has also been reported. We propose that the maximum-likelihood estimation is a more appropriate statistical method for the determination of normal range from this type of data (Type I censored data). With this method, the mean and standard deviation, and hence the tolerance limits, can be estimated. We used the maximum-likelihood estimation method to determine the normal range of serum thyrotropin values obtained from 93 healthy subjects, based on a log normal distribution. Although the serum thyrotropin content was undetectable in 14% of the subjects, a normal range could be calculated. Using tolerance limits for 95% coverage of the population with 90% confidence, we calculated the normal range of thyrotropin to be 0.51- 5.75 milliunits/L, with a mean value of 1.71 milliunits/L, and predicted that 91.4% of undetectable serum thyrotropin values will fall within the normal range.


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